The Mortar Method in the Wavelet Context

Silvia Bertoluzza; Valérie Perrier

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 35, Issue: 4, page 647-673
  • ISSN: 0764-583X

Abstract

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This paper deals with the use of wavelets in the framework of the Mortar method. We first review in an abstract framework the theory of the mortar method for non conforming domain decomposition, and point out some basic assumptions under which stability and convergence of such method can be proven. We study the application of the mortar method in the biorthogonal wavelet framework. In particular we define suitable multiplier spaces for imposing weak continuity. Unlike in the classical mortar method, such multiplier spaces are not a subset of the space of traces of interior functions, but rather of their duals. For the resulting method, we provide with an error estimate, which is optimal in the geometrically conforming case.

How to cite

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Bertoluzza, Silvia, and Perrier, Valérie. "The Mortar Method in the Wavelet Context." ESAIM: Mathematical Modelling and Numerical Analysis 35.4 (2010): 647-673. <http://eudml.org/doc/197416>.

@article{Bertoluzza2010,
abstract = { This paper deals with the use of wavelets in the framework of the Mortar method. We first review in an abstract framework the theory of the mortar method for non conforming domain decomposition, and point out some basic assumptions under which stability and convergence of such method can be proven. We study the application of the mortar method in the biorthogonal wavelet framework. In particular we define suitable multiplier spaces for imposing weak continuity. Unlike in the classical mortar method, such multiplier spaces are not a subset of the space of traces of interior functions, but rather of their duals. For the resulting method, we provide with an error estimate, which is optimal in the geometrically conforming case. },
author = {Bertoluzza, Silvia, Perrier, Valérie},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Domain decomposition; mortar method; wavelet approximation.; domain decomposition; wavelet approximation; stability; convergence; error estimate},
language = {eng},
month = {3},
number = {4},
pages = {647-673},
publisher = {EDP Sciences},
title = {The Mortar Method in the Wavelet Context},
url = {http://eudml.org/doc/197416},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Bertoluzza, Silvia
AU - Perrier, Valérie
TI - The Mortar Method in the Wavelet Context
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 4
SP - 647
EP - 673
AB - This paper deals with the use of wavelets in the framework of the Mortar method. We first review in an abstract framework the theory of the mortar method for non conforming domain decomposition, and point out some basic assumptions under which stability and convergence of such method can be proven. We study the application of the mortar method in the biorthogonal wavelet framework. In particular we define suitable multiplier spaces for imposing weak continuity. Unlike in the classical mortar method, such multiplier spaces are not a subset of the space of traces of interior functions, but rather of their duals. For the resulting method, we provide with an error estimate, which is optimal in the geometrically conforming case.
LA - eng
KW - Domain decomposition; mortar method; wavelet approximation.; domain decomposition; wavelet approximation; stability; convergence; error estimate
UR - http://eudml.org/doc/197416
ER -

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Citations in EuDML Documents

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  1. Saloua Mani Aouadi, Jamil Satouri, Mortar spectral method in axisymmetric domains
  2. Saloua Mani Aouadi, Jamil Satouri, Mortar spectral method in axisymmetric domains
  3. Zakaria Belhachmi, Christine Bernardi, Andreas Karageorghis, Mortar spectral element discretization of the Laplace and Darcy equations with discontinuous coefficients
  4. Christine Bernardi, Frédéric Hecht, Olivier Pironneau, Coupling Darcy and Stokes equations for porous media with cracks
  5. Christine Bernardi, Frédéric Hecht, Olivier Pironneau, Coupling Darcy and Stokes equations for porous media with cracks

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